Number of Moles of Forsterite

Oct 13, 2025 by miodeya.com 145 views

Introduction

Forsterite, also known as magnesium silicate, is a mineral composed of magnesium, silicon, and oxygen atoms. Its chemical formula is $\left( Mg_2SiO_4 \right)$ . In this article, we will calculate the number of magnesium atoms in a 60.0 g sample of forsterite. This calculation will involve determining the molar mass of forsterite, the number of moles of forsterite in the sample, and finally, the number of magnesium atoms in the sample.

Molar Mass of Forsterite

To calculate the number of magnesium atoms in forsterite, we first need to determine the molar mass of forsterite. The molar mass of a compound is the sum of the atomic masses of its constituent elements. The atomic masses of magnesium, silicon, and oxygen are 24.31 g/mol, 28.09 g/mol, and 16.00 g/mol, respectively.

The molar mass of forsterite can be calculated as follows:

M_{\text{forsterite}} = 2 \times M_{\text{magnesium}} + M_{\text{silicon}} + 4 \times M_{\text{oxygen}}

M_{\text{forsterite}} = 2 \times 24.31 \text{ g/mol} + 28.09 \text{ g/mol} + 4 \times 16.00 \text{ g/mol}

M_{\text{forsterite}} = 48.62 \text{ g/mol} + 28.09 \text{ g/mol} + 64.00 \text{ g/mol}

M_{\text{forsterite}} = 140.71 \text{ g/mol}

Number of Moles of Forsterite

Now that we have the molar mass of forsterite, we can calculate the number of moles of forsterite in the 60.0 g sample. The number of moles of a substance can be calculated using the formula:

n = \frac{m}{M}

where $n$ is the number of moles, $m$ is the mass of the substance, and $M$ is the molar mass of the substance.

Plugging in the values, we get:

n = \frac{60.0 \text{ g}}{140.71 \text{ g/mol}}

n = 0.426 \text{ mol}

Number of Magnesium Atoms

Now that we have the number of moles of forsterite, we can calculate the number of magnesium atoms in the sample. The number of magnesium atoms in a mole of forsterite is 2, since the chemical formula of forsterite is $\left( Mg_2SiO_4 \right)$ . Therefore, the number of magnesium atoms in the sample is:

N = n \times N_A \times 2

where $N$ is the number of magnesium atoms, $n$ is the number of moles of forsterite, $N_A$ is Avogadro's number (6.022 x 10^23 atoms/mol), and 2 is the number of magnesium atoms per mole of forsterite.

Plugging in the values, we get:

N = 0.426 \text{ mol} \times 6.022 \times 10^{23} \text{ atoms/mol} \times 2

N = 5.13 \times 10^{24} \text{ atoms}

Conclusion

In this article, we calculated the number of magnesium atoms in a 60.0 g sample of forsterite. We first determined the molar mass of forsterite, then calculated the number of moles of forsterite in the sample, and finally, calculated the number of magnesium atoms in the sample. The result is 5.13 x 10^24 atoms.

References

CRC Handbook of Chemistry and Physics, 97th Edition
IUPAC, "Atomic Weights of the Elements 2016 (IUPAC Technical Report)"
NIST, "Atomic Weights of the Elements 2016"

Note

Frequently Asked Questions

Q: What is forsterite and why is it important?

A: Forsterite, also known as magnesium silicate, is a mineral composed of magnesium, silicon, and oxygen atoms. Its chemical formula is $\left( Mg_2SiO_4 \right)$ . Forsterite is an important mineral in geology and chemistry, and it has various applications in industries such as ceramics, glass, and electronics.

Q: How do I calculate the number of magnesium atoms in forsterite?

A: To calculate the number of magnesium atoms in forsterite, you need to determine the molar mass of forsterite, the number of moles of forsterite in the sample, and finally, the number of magnesium atoms in the sample. You can use the formula:

N = n \times N_A \times 2

Q: What is the molar mass of forsterite?

A: The molar mass of forsterite is 140.71 g/mol. You can calculate it by summing the atomic masses of its constituent elements: magnesium (24.31 g/mol), silicon (28.09 g/mol), and oxygen (16.00 g/mol).

Q: How do I determine the number of moles of forsterite in the sample?

A: To determine the number of moles of forsterite in the sample, you can use the formula:

n = \frac{m}{M}

where $n$ is the number of moles, $m$ is the mass of the substance, and $M$ is the molar mass of the substance.

Q: What is Avogadro's number and why is it important?

A: Avogadro's number is a fundamental constant in chemistry that represents the number of particles (atoms or molecules) in one mole of a substance. It is equal to 6.022 x 10^23 particles/mol. Avogadro's number is important because it allows us to calculate the number of particles in a sample of a substance.

Q: Can I use this calculation for other minerals or compounds?

A: Yes, you can use this calculation for other minerals or compounds as long as you know their chemical formulas and molar masses. However, you need to adjust the calculation accordingly to account for the different number of atoms of each element in the compound.

Q: What are some common applications of forsterite?

A: Forsterite has various applications in industries such as ceramics, glass, and electronics. It is also used in the production of refractory materials, abrasives, and pigments.

Q: Can I calculate the number of magnesium atoms in forsterite using other methods?

A: Yes, you can calculate the number of magnesium atoms in forsterite using other methods such as X-ray diffraction, electron microscopy, or nuclear magnetic resonance (NMR) spectroscopy. However, these methods may require specialized equipment and expertise.

Conclusion

In this article, we have provided a Q&A section to help you understand the calculation of the number of magnesium atoms in forsterite. We have covered various topics such as the importance of forsterite, the calculation of the number of moles of forsterite, and the use of Avogadro's number. We hope that this article has been helpful in answering your questions and providing you with a better understanding of the calculation of the number of magnesium atoms in forsterite.